1,720,985 research outputs found
Universality class of the two-dimensional polymer collapse transition
Full text linkThe nature of the θ point for a polymer in two dimensions has long been debated, with a variety of candidates put forward for the critical exponents. This includes those derived by Duplantier and Saleur for an exactly solvable model. We use a representation of the problem via the CP[superscript N−1]σ model in the limit N → 1 to determine the stability of this critical point. First we prove that the Duplantier-Saleur (DS) critical exponents are robust, so long as the polymer does not cross itself: They can arise in a generic lattice model and do not require fine-tuning. This resolves a longstanding theoretical question. We also address an apparent paradox: Two different lattice models, apparently both in the DS universality class, show different numbers of relevant perturbations, apparently leading to contradictory conclusions about the stability of the DS exponents. We explain this in terms of subtle differences between the two models, one of which is fine-tuned (and not strictly in the DS universality class). Next we allow the polymer to cross itself, as appropriate, e.g., to the quasi-two-dimensional case. This introduces an additional independent relevant perturbation, so we do not expect the DS exponents to apply. The exponents in the case with crossings will be those of the generic tricritical O(n) model at n = 0 and different from the case without crossings. We also discuss interesting features of the operator content of the CP[superscript N−1] model. Simple geometrical arguments show that two operators in this field theory, with very different symmetry properties, have the same scaling dimension for any value of N (or, equivalently, any value of the loop fugacity). Also we argue that for any value of N the CP[superscript N−1] model has a marginal odd-parity operator that is related to the winding angle.Gordon and Betty Moore Foundation. EPiQS Initiative (Grant GBMF4303
Topological paramagnetism in frustrated spin-1 Mott insulators
Full text linkTime-reversal-protected three-dimensional (3D) topological paramagnets are magnetic analogs of the celebrated 3D topological insulators. Such paramagnets have a bulk gap and no exotic bulk excitations, but have non-trivial surface states protected by symmetry. We propose that frustrated spin-1 quantum magnets are a natural setting for realizing such states in three dimensions. We describe a physical picture of the ground-state wave function for such a spin-1 topological paramagnet in terms of loops of fluctuating Haldane chains with nontrivial linking phases. We illustrate some aspects of such loop gases with simple exactly solvable models. We also show how 3D topological paramagnets can be very naturally accessed within a slave particle description of a spin-1 magnet. Specifically, we construct slave-particle mean-field states which are naturally driven into the topological paramagnet upon including fluctuations. We propose bulk projected wave functions for the topological paramagnet based on this slave-particle description. An alternate slave-particle construction leads to a stable U(1) quantum spin liquid from which a topological paramagnet may be accessed by condensing the emergent magnetic monopole excitation of the spin liquid.Gordon and Betty Moore Foundation (EPiQS Initiative Grant GBMF4303)National Science Foundation (U.S.) (Grant NSF DMR-1305741)Simons Foundation (Simons Investigator Award
Topological Constraints in Directed Polymer Melts
Full text linkPolymers in a melt may be subject to topological constraints, as in the example of unlinked polymer rings. How to do statistical mechanics in the presence of such constraints remains a fundamental open problem. We study the effect of topological constraints on a melt of directed polymers, using simulations of a simple quasi-2D model. We find that fixing the global topology of the melt to be trivial changes the polymer conformations drastically. Polymers of length L wander in the transverse direction only by a distance of order (lnL)[superscript ζ] with ζ≃1.5. This is strongly suppressed in comparison with the Brownian L[superscript 1/2] scaling which holds in the absence of the topological constraint. It is also much smaller than the predictions of standard heuristic approaches—in particular the L[superscript 1/4] of a mean-field-like “array of obstacles” model—so our results present a sharp challenge to theory. Dynamics are also strongly affected by the constraints, and a tagged monomer in an infinite system performs logarithmically slow subdiffusion in the transverse direction. To cast light on the suppression of the strands’ wandering, we analyze the topological complexity of subregions of the melt: the complexity is also logarithmically small, and is related to the wandering by a power law. We comment on insights the results give for 3D melts, directed and nondirected.Spain. Ministerio de Economia y Competitividad (European Union FEDER Grant FIS2012-38206)Spain. Ministerio de Educacion, Cultura y Deporte. Formacion de Profesorado Universitario (Grant AP2009-0668)MIT Department of Physics Pappalardo ProgramGordon and Betty Moore Foundation. EPiQS Initiative (Grant GBMF4303
Quantum Entanglement Growth under Random Unitary Dynamics
No full textCharacterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the “entanglement tsunami” in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated Kardar-Parisi-Zhang (KPZ) equation. The mean entanglement grows linearly in time, while fluctuations grow like (time)[superscript 1/3] and are spatially correlated over a distance ∝(time)[superscript 2/3]. We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i) a stochastic model of a growing surface, (ii) a “minimal cut” picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii) a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the “velocity” of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the well-studied problem of pinning of a membrane or domain wall by disorder. Subject Areas: Condensed Matter Physics, Quantum Information, Statistical PhysicsGordon and Betty Moore Foundation (Grant GBMF4303)Engineering and Physical Sciences Research Council (Grant EP/N028678/1)Kavli Institute for Theoretical Physics (Graduate Fellows Program)United States. Department of Energy. Division of Materials Sciences and Engineering (Award DE-SC0010526)Massachusetts Institute of Technology (MIT Pappalardo Fellowship in Physics
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
Full text linkNumerical studies of the transition between Néel and valence bond solid phases in two-dimensional quantum antiferromagnets give strong evidence for the remarkable scenario of deconfined criticality, but display strong violations of finite-size scaling that are not yet understood. We show how to realize the universal physics of the Néel–valence-bond-solid (VBS) transition in a three-dimensional classical loop model (this model includes the subtle interference effect that suppresses hedgehog defects in the Néel order parameter). We use the loop model for simulations of unprecedentedly large systems (up to linear size L = 512). Our results are compatible with a continuous transition at which both Néel and VBS order parameters are critical, and we do not see conventional signs of first-order behavior. However, we show that the scaling violations are stronger than previously realized and are incompatible with conventional finite-size scaling, even if allowance is made for a weakly or marginally irrelevant scaling variable. In particular, different approaches to determining the anomalous dimensions η[subscript VBS] and η[subscript Néel] yield very different results. The assumption of conventional finite-size scaling leads to estimates that drift to negative values at large sizes, in violation of the unitarity bounds. In contrast, the decay with distance of critical correlators on scales much smaller than system size is consistent with large positive anomalous dimensions. Barring an unexpected reversal in behavior at still larger sizes, this implies that the transition, if continuous, must show unconventional finite-size scaling, for example, from an additional dangerously irrelevant scaling variable. Another possibility is an anomalously weak first-order transition. By analyzing the renormalization group flows for the noncompact CP[superscript n-1] field theory (the n-component Abelian Higgs model) between two and four dimensions, we give the simplest scenario by which an anomalously weak first-order transition can arise without fine-tuning of the Hamiltonian.Engineering and Physical Sciences Research Council (Grant EP/I032487/1)Spain. Ministerio de Economia y Competitividad (FEDER Grant FIS2012-38206)Spain. Ministerio de Educacion, Cultura y Deporte. Formacion de Profesorado Universitario (Grant AP2009-0668)Gordon and Betty Moore Foundation. EPiQS Initiative (Grant GBMF4303
Emergent SO(5) Symmetry at the Néel to Valence-Bond-Solid Transition
Full text linkWe show numerically that the “deconfined” quantum critical point between the Néel antiferromagnet and the columnar valence-bond solid, for a square lattice of spin 1/2, has an emergent SO(5) symmetry. This symmetry allows the Néel vector and the valence-bond solid order parameter to be rotated into each other. It is a remarkable (2+1)-dimensional analogue of the SO(4)=[SU(2)×SU(2)]/Z[subscript 2] symmetry that appears in the scaling limit for the spin-1/2 Heisenberg chain. The emergent SO(5) symmetry is strong evidence that the phase transition in the (2+1)-dimensional system is truly continuous, despite the violations of finite-size scaling observed previously in this problem. It also implies surprising relations between correlation functions at the transition. The symmetry enhancement is expected to apply generally to the critical two-component Abelian Higgs model (noncompact CP[superscript 1] model). The result indicates that in three dimensions there is an SO(5)-symmetric conformal field theory that has no relevant singlet operators, so is radically different from conventional Wilson-Fisher-type conformal field theories.Gordon and Betty Moore Foundation. EPiQS Initiative (Grant GBMF4303)Engineering and Physical Sciences Research Council (Grant EP/I032487/1)Spain. Ministerio de Economia y Competitividad (FEDER Grant FIS2012-38206)Spain. Ministerio de Educacion, Cultura y Deporte. Formacion de Profesorado Universitario (Grant AP2009-0668
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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